Resonant conversion of massless neutrinos in supernovae

It has been noted for a long time that, in some circumstances, massless neutrinos may be mixed in the leptonic charged current. Conventional neutrino oscillation searches in vacuum are insensitive to this mixing. We discuss the effects of resonant massless-neutrino conversions in the dense medium of a supernova. In particular, we show how the detected ${\overline{\nu }}_e$ energy spectra from SN 1987A and the supernova $r$-process nucleo-synthesis may be used to provide very stringent constraints on the mixing of massless neutrinos.